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This paper considers a linear precoding scheme that achieves near optimal sum rate. While the minimum mean square error (MMSE) precoding provides the better MSE performance at all signal-to-noise ratio (SNR) than the zero forcing (ZF) precoding, its sum rate shows superior performance to ZF precoding at low SNR but inferior performance to ZF precoding at high SNR. From this observation, we first develop a near sum rate optimal linear precoding scheme for the case of single receive antenna per user. The resulting precoding scheme regularizes ZF precoding to maximize the sum rate, resulting in better sum rate performance than both ZF precoding and MMSE precoding at all SNR. The proposed scheme is extended to the case of the multiple receive antennas, and it shows the better sum rate performance than the block diagonalization (BD) scheme at all SNR.